Amy has seven cards numbered 1, 2, 3, 4, 5, 6, and 7. She randomly deals three each to Bill and Celia, keeping one for
herself. All three people then look at their cards. Can Bill and Celia communicate with each other, in the presence of Amy, so that
Bill and Celia can each determine what cards the other holds, but Amy will not know who holds any given card, other than the
one that she herself holds?

Claims Data
Christopher Yaure's puzzle involved claim count data on five 12-month policies. He was supplied with claim counts on
the five policies, and was subsequently provided with a corrected claim count for one policy. In the corrected claim count data,
the mode was exactly the same as in the original data, the mean claim count was exactly 1 larger than the original data, the
variance was exactly 2 larger, and the median was exactly 3 larger. Additionally, the final counts satisfied what Christopher called
the "Rule of 3s":

The final number of claims for each policy was a multiple of 3.
The ratio of high to low number of claims was 3. Exactly 3 policies had an average of more than 3 claims per month.

The question was, what was the final claims frequency distribution?

A number of solvers determined that the final counts were 15, 36, 39, 45, and 45, and that the 39 had originally been
reported as 34.